Off-shell properties of the two-nucleontmatrix

Abstract

The off-shell properties of two-nucleon t matrices are studied for both uncoupled and coupled channels. Complex t matrices have been obtained using both matrix inversion and continued fraction techniques of solution and predicated upon a standard phenomenological form (Reid}, a meson exchange model (Paris), and a new phenomenological form that we have developed, of the two-nucleon interaction. The off-shell t matrices from these interactions are very similar whenever they give essentially the same phase shifts at all energies. When they do not, the associated offshell t matrices diverge so substantially that any data depending upon these off-shell t matrices will differentiate between the interactions. trix. Secondly we investigate alternative numerical techniques to have a reliable evaluation of the off-shell properties and finally we analyze the differences we find in the off-shell behavior of various internucleon forces.The first of the concerns, the two nucleon problem, has been studied extensively over the past 30 years both from a purely phenomenological viewpoint as well as with theories founded upon meson exchanges. More recently, new schemes which are hybrids of quantum chromodynamics (QCD) at short distances with one boson exchange potentials for the larger separations have been proposed. The Hamada-Johnston and Reid potentials are representative of the phenomenological viewpoint and are interactions still in use. Of the more modern NN interactions determined from field theoretic or dispersion relations techniques, the Bonn and Paris are widely quoted in literature, while the QCD based models are as yet not so favored. %hatever be the basis, all such NN interactions are determined from fits to the elastic NN phase shifts and the properties of the deuteron, ' such fits varying in quality between different interactions and for different twobody channels. The critical features of all interactions, whether contrived or derived, are the form factors. For this reason we consider herein the Reid interaction as being representative of the usual phenomenologically based interactions, the Paris as being representative of the derived interactions and a third which we have developed from a recent, momentum space, phenomenological model. ' Our model interaction has a form factor with momentum transfer dependence additional to the usual one boson exchange potentials (OBEP} and is defined to obtain the best possible fits to all partial wave 37 934

Medium corrections to nucleon-nucleon interactions

“…The f ratios at 200 MeV (CM) are exceptional. But as with previous studies of free N N t matrices (Amos et al 1988a) in this region of energy we know that the on-shell R matrix is small and as this is the denominator of the f ratio, small (absolute) changes in values as one moves off the energy shell will reflect in large f ratio values.…”

Separable expansions of theNNtmatrix via exact half-off-the-energy-shell methods

“…Thus, even though the difFerences between the exact and separable representation values are very small, any such difFerence is magnified greatly by the ratio. This is not unlike the problem encountered by others [34] when comparing K and t matrices and using the Kowalski -Noyes f ratios [24,35]. The results between 200 and 250 MeV reveal that the SSM gives a much better approximation to the iSO t matrices than the method of Ref.…”

Parametrization scheme for effective interactions

“…From those functions half oH'-shell t matrices can be obtained and then the fully oA'-shell values follow from an integral equation [20]. At present our inversion studies are incomplete whence herein we make use of the Paris [6] and Bonn [7] potentials for computation of t matrices either in momentum [19,21] or in coordinate [20] space. As indicated in Sec.…”